# two-way ANOVA - how to conduct post-hoc tests?

Conducted a two-way ANOVA and got a main effect of sound manipulation onto perceived diagnosticity.

Anova Table (Type III tests)

Response: PD
Sum Sq  Df  F value    Pr(>F)
(Intercept)           2056.20   1 784.8304 < 2.2e-16 ***
Manipulation            40.70   2   7.7668 0.0006036 ***
Product                  6.47   1   2.4692 0.1180734
Manipulation:Product     0.59   2   0.1126 0.8935742
Residuals              419.19 160
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


I conducted planned comparisons to see how the congruent (KON) compares to the other two conditions combined (ALL=no sound and incongruent).

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)                     3.54791    0.12664  28.015  < 2e-16 ***
ManipulationcALL_KON            0.33842    0.08811   3.841 0.000176 ***
ManipulationcINK_NS            -0.17477    0.15757  -1.109 0.269020
Product1                       -0.19900    0.12664  -1.571 0.118073
ManipulationcALL_KON:Product1  -0.03812    0.08811  -0.433 0.665815
ManipulationcINK_NS:Product1   -0.02662    0.15757  -0.169 0.866052
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.619 on 160 degrees of freedom
Multiple R-squared:  0.09894,   Adjusted R-squared:  0.07078
F-statistic: 3.514 on 5 and 160 DF,  p-value: 0.004848


Now I would like to contrast the "congruent" sound condition with the "incongruent" one and the "no sound" one, always on the product level, i.e. once for the towel and once for the tv. I would like to use post-hoc tests to do so. Yet when I use TukeyHSD in R, it collapses the product, so it compares the sound manipulation regardless of the product.

How could I make sensible post-hoc comparisons or should I use another form of comparison?

emm = emmeans(model, ~ Manipulation*Product)